Suppose that we have 11 observations from the convolution model Y = X + £, where X and £ are the independent unobservable random variables, and £ is measurement error with a known distribution. We will discuss the asymptotic normality for deconvolving kernel density estimators of the unknown density f x 0 of X by assuming either the tail of the characteristic function of £ behaves as II I~Oexp(...

This paper presents some asymptotical results of the Hermite Normality test previously introduced. We show that the Hermite statistic S H is distributed under the null hypothesis as a quadratic form of normal variates and under the nonnull hypothesis as normal. The special case of tests with two polynomials is studied in details. Finally, we give some considerations for the choice of a best Her...

In 1948, W. Hoeffding introduced a large class of unbiased estimators called U -statistics, defined as the average value of a real-valued m-variate function h calculated at all possible sets of m points from a random sample. In the present paper, we investigate the corresponding robust analogue which we call U -quantile-statistics. We are concerned with the asymptotic behavior of the sample p-q...